If A ⊆ B and B − A = ∅, which conclusion follows?
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Answer and explanation
Correct answer: A = B
The statement A ⊆ B says that every element of A belongs to B. The condition B − A = ∅ says that B has no element outside A; therefore every element of B also belongs to A, so B ⊆ A. Since both A ⊆ B and B ⊆ A hold, the two sets are equal. Thus A = B, and option A is correct. No information requires A to be empty.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The statement A ⊆ B says that every element of A belongs to B. The condition B − A = ∅ says that B has no element outside A; therefore every element of B also belongs to A, so B ⊆ A. Since both A ⊆ B and B ⊆ A hold, the two sets are equal. Thus A = B, and option A is correct. No information requires A to be empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
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